Hello Evan,
While the aperture gain in the 127 Mak isn't all that much, yes it will be a significant improvement in optical quality over the 4" achro. It will allow you to go to 250X without showing chromatic aberration as Raymo says.
As for the cooling, DON'T let it cool down!
The whole problem for Maks & SCTs in cooling is the heat plume that develops because of the warm primary mirror & baffle and the cold metal tube. So, if the tube is not allowed to cool, say by wrapping it in an insulating wrap, the temp differential between tube and primary mirror & baffle won't occur, and hence no heat plume. And you can rip the max magnification from the Mak from the very start of your viewing session.
I've been doing this for several years now, first with my orange tube SCT, through to the 7" Intes Mak I had and now with the 9" Santel Mak I use. No cooling down time, but straight to work.
For the Maks I made the insulating wrap-come-dewshield out of white Coreflute. Where it extends over the corrector I lined the inside of the wrap with black contact felt. The colour of the wrap is vitally important!!! DO NOT USE A BLACK OR DARK MATERIAL! Black cools down to below the ambient temperature and as a result will both act to accelerate the cooling of the tube ( ie induce the heat plume we want to avoid) plus it will attract dew a whole lot faster than white or a silvered surface.
The Coreflute wrap is made by cutting down every second cell on the outside surface. This allows the wrap to easily roll on itself and around the tube. How far out from the corrector you make the dewshield part, the minimum I would suggest is the aperture of the scope. This wrap will also extend the time the corrector stays dew free compared to just having a dewshield that only extends out from the corrector. It won't totally prevent dew, but will markedly extend how long the scope goes without dew forming. I also cut the necessary slots and holes to accommodate the handle, finder scope shoes and anchor points for the dovetail plate so the whole of the scope is wrapped.
Some people have also used a type of aluminized building insulation that is on a rubber mat/sheet. It doesn't need to look pretty. It just needs to work.
Alex.